Transport Based Image Morphing with Intensity Modulation

  • Jan Maas
  • Martin Rumpf
  • Stefan SimonEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10302)


We present a generalized optimal transport model in which the mass-preserving constraint for the \(L^2\)-Wasserstein distance is relaxed by introducing a source term in the continuity equation. The source term is also incorporated in the path energy by means of its squared \(L^2\)-norm in time of a functional with linear growth in space. This extension of the original transport model enables local density modulations, which is a desirable feature in applications such as image warping and blending. A key advantage of the use of a functional with linear growth in space is that it allows for singular sources and sinks, which can be supported on points or lines. On a technical level, the \(L^2\)-norm in time ensures a disintegration of the source in time, which we use to obtain the well-posedness of the model and the existence of geodesic paths. The numerical discretization is based on the proximal splitting approach [18] and selected numerical test cases show the potential of the proposed approach. Furthermore, the approach is applied to the warping and blending of textures.


Optimal transport Texture morphing Generalized Wasserstein distance Proximal splitting 

Supplementary material

427343_1_En_45_MOESM1_ESM.pdf (177 kb)
Supplementary material 1 (pdf 176 KB)

Supplementary material 2 (mp4 8301 KB)


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institute of Science and Technology AustriaKlosterneuburgAustria
  2. 2.Institute for Numerical SimulationUniversität BonnBonnGermany

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